Question

sometimes two angles pair up to make a larger angle. you can assume that adding the measures of the smaller angles will equal to the measure of the larger angle.
postulate 2: angle addition postulate
if ( s ) is the interior of ( angle pqr ), then ( mangle pqr=mangle pqs + mangle sqr ).
pairs of angles can have special relationships. the measurement of the angles determines the relationship.
classifying pairs of angles
complementary angles are two angles whose measures have a sum of ( 90^{circ} ).
supplementary angles are two angles whose measures have a sum of ( 180^{circ} )
your turn
determine if the angle pairs are complementary, supplementary or neither given ( mangle pro = 99^{circ} ), ( mangle prq = 81^{circ} ), ( mangle prs = 9^{circ} ), and ( mangle ors = 90^{circ} ).

1. ( angle prq ) and ( angle pro ) are ____________.
2. ( angle ors ) and ( angle prs ) are ____________.
3. ( angle ors ) and ( angle srq ) are ____________.
4. ( angle prq ) and ( angle prs ) are ____________.

Explanation:

Step1: Check for supplementary angles (sum \(180^{\circ}\))

For \(\angle PRQ\) and \(\angle PRO\), \(m\angle PRQ + m\angle PRO=81^{\circ}+99^{\circ}=180^{\circ}\).

Step2: Check for complementary angles (sum \(90^{\circ}\))

For \(\angle ORS\) and \(\angle PRS\), \(m\angle ORS + m\angle PRS = 90^{\circ}+9^{\circ}=99^{\circ}
eq90^{\circ}\). For \(\angle ORS\) and \(\angle SRQ\), assume \(m\angle SRQ=m\angle PRQ + m\angle PRS=81^{\circ}+9^{\circ}=90^{\circ}\), then \(m\angle ORS + m\angle SRQ=90^{\circ}+90^{\circ}=180^{\circ}\). For \(\angle PRQ\) and \(\angle PRS\), \(m\angle PRQ + m\angle PRS=81^{\circ}+9^{\circ}=90^{\circ}\).

Answer:

1. Supplementary angles
2. Neither
3. Supplementary angles
4. Complementary angles